Abstract
We study the black string solutions in the Einstein-Gauss-Bonnet(EGB) theory at large D. By using the 1/D expansion in the near horizon region we derive the effective equations that describe the dynamics of the EGB black strings. The uniform and non-uniform black strings are obtained as the static solutions of the effective equations. From the perturbation analysis of the effective equations, we find that thin EGB black strings suffer from the Gregory-Laflamme instablity and the GB term weakens the instability when the GB coefficient is small, however, when the GB coefficient is large the GB term enhances the instability. Furthermore, we numerically solve the effective equations to study the non-linear instability. It turns out that the thin black strings are unstable to developing inhomogeneities along their length, and at late times they asymptote to the stable non-uniform black strings. The behavior is qualitatively similar to the case in the Einstein gravity. Compared with the black string instability in the Einstein gravity at large D, when the GB coefficient is small the time needed to reach to final state increases, but when the GB coefficient is large the time to reach to final state decreases. Starting from the point of view in which the effective equations can be interpreted as the equations for the dynamical fluid, we evaluate the transport coefficients and find that the ratio of the shear viscosity and the entropy density agrees with that obtained previously in the membrane paradigm after taking the large D limit.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
R. Emparan and H.S. Reall, Black holes in higher dimensions, Living Rev. Rel. 11 (2008) 6 [arXiv:0801.3471] [INSPIRE].
G.T. Horowitz, Black holes in higher dimensions, Cambridge University Press, Cambridge U.K., (2012) [INSPIRE].
R. Gregory and R. Laflamme, Black strings and p-branes are unstable, Phys. Rev. Lett. 70 (1993) 2837 [hep-th/9301052] [INSPIRE].
Q.-Q. Jiang and S.-Q. Wu, Hawking radiation from rotating black holes in anti-de Sitter spaces via gauge and gravitational anomalies, Phys. Lett. B 647 (2007) 200 [hep-th/0701002] [INSPIRE].
S.S. Gubser, On nonuniform black branes, Class. Quant. Grav. 19 (2002) 4825 [hep-th/0110193] [INSPIRE].
E. Sorkin, A critical dimension in the black string phase transition, Phys. Rev. Lett. 93 (2004) 031601 [hep-th/0402216] [INSPIRE].
T. Wiseman, Static axisymmetric vacuum solutions and nonuniform black strings, Class. Quant. Grav. 20 (2003) 1137 [hep-th/0209051] [INSPIRE].
B. Kleihaus, J. Kunz and E. Radu, New nonuniform black string solutions, JHEP 06 (2006) 016 [hep-th/0603119] [INSPIRE].
E. Sorkin, Non-uniform black strings in various dimensions, Phys. Rev. D 74 (2006) 104027 [gr-qc/0608115] [INSPIRE].
M. Headrick, S. Kitchen and T. Wiseman, A new approach to static numerical relativity and its application to Kaluza-Klein black holes, Class. Quant. Grav. 27 (2010) 035002 [arXiv:0905.1822] [INSPIRE].
P. Figueras, K. Murata and H.S. Reall, Stable non-uniform black strings below the critical dimension, JHEP 11 (2012) 071 [arXiv:1209.1981] [INSPIRE].
M. Kalisch and M. Ansorg, Pseudo-spectral construction of non-uniform black string solutions in five and six spacetime dimensions, Class. Quant. Grav. 33 (2016) 215005 [arXiv:1607.03099] [INSPIRE].
M. Kalisch, S. Möckel and M. Ammon, Critical behavior of the black hole/black string transition, JHEP 08 (2017) 049 [arXiv:1706.02323] [INSPIRE].
L. Lehner and F. Pretorius, Black strings, low viscosity fluids and violation of cosmic censorship, Phys. Rev. Lett. 105 (2010) 101102 [arXiv:1006.5960] [INSPIRE].
L. Lehner and F. Pretorius, Final state of Gregory-Laflamme instability, arXiv:1106.5184 [INSPIRE].
R. Emparan, R. Suzuki and K. Tanabe, The large D limit of general relativity, JHEP 06 (2013) 009 [arXiv:1302.6382] [INSPIRE].
R. Emparan, R. Suzuki and K. Tanabe, Decoupling and non-decoupling dynamics of large D black holes, JHEP 07 (2014) 113 [arXiv:1406.1258] [INSPIRE].
R. Emparan, T. Shiromizu, R. Suzuki, K. Tanabe and T. Tanaka, Effective theory of black holes in the 1/D expansion, JHEP 06 (2015) 159 [arXiv:1504.06489] [INSPIRE].
R. Suzuki and K. Tanabe, Stationary black holes: large D analysis, JHEP 09 (2015) 193 [arXiv:1505.01282] [INSPIRE].
S. Bhattacharyya, A. De, S. Minwalla, R. Mohan and A. Saha, A membrane paradigm at large D, JHEP 04 (2016) 076 [arXiv:1504.06613] [INSPIRE].
S. Bhattacharyya, M. Mandlik, S. Minwalla and S. Thakur, A charged membrane paradigm at large D, JHEP 04 (2016) 128 [arXiv:1511.03432] [INSPIRE].
Y. Dandekar, A. De, S. Mazumdar, S. Minwalla and A. Saha, The large D black hole membrane paradigm at first subleading order, JHEP 12 (2016) 113 [arXiv:1607.06475] [INSPIRE].
R. Suzuki and K. Tanabe, Non-uniform black strings and the critical dimension in the 1/D expansion, JHEP 10 (2015) 107 [arXiv:1506.01890] [INSPIRE].
R. Emparan, R. Suzuki and K. Tanabe, Evolution and end point of the black string instability: large D solution, Phys. Rev. Lett. 115 (2015) 091102 [arXiv:1506.06772] [INSPIRE].
K. Tanabe, Black rings at large D, JHEP 02 (2016) 151 [arXiv:1510.02200] [INSPIRE].
K. Tanabe, Instability of the de Sitter Reissner-Nordström black hole in the 1/D expansion, Class. Quant. Grav. 33 (2016) 125016 [arXiv:1511.06059] [INSPIRE].
R. Emparan, K. Izumi, R. Luna, R. Suzuki and K. Tanabe, Hydro-elastic complementarity in black branes at large D, JHEP 06 (2016) 117 [arXiv:1602.05752] [INSPIRE].
K. Tanabe, Elastic instability of black rings at large D, arXiv:1605.08116 [INSPIRE].
M. Rozali and A. Vincart-Emard, On brane instabilities in the large D limit, JHEP 08 (2016) 166 [arXiv:1607.01747] [INSPIRE].
Y. Dandekar, S. Mazumdar, S. Minwalla and A. Saha, Unstable ‘black branes’ from scaled membranes at large D, JHEP 12 (2016) 140 [arXiv:1609.02912] [INSPIRE].
B. Chen, P.-C. Li and Z.-Z. Wang, Charged black rings at large D, JHEP 04 (2017) 167 [arXiv:1702.00886] [INSPIRE].
R. Emparan, T. Harmark, V. Niarchos and N.A. Obers, World-volume effective theory for higher-dimensional black holes, Phys. Rev. Lett. 102 (2009) 191301 [arXiv:0902.0427] [INSPIRE].
R. Emparan, T. Harmark, V. Niarchos and N.A. Obers, Essentials of blackfold dynamics, JHEP 03 (2010) 063 [arXiv:0910.1601] [INSPIRE].
B. Zwiebach, Curvature squared terms and string theories, Phys. Lett. B 156 (1985) 315 [INSPIRE].
D.G. Boulware and S. Deser, String generated gravity models, Phys. Rev. Lett. 55 (1985) 2656 [INSPIRE].
J.T. Wheeler, Symmetric solutions to the Gauss-Bonnet extended Einstein equations, Nucl. Phys. B 268 (1986) 737 [INSPIRE].
G. Giribet, J. Oliva and R. Troncoso, Simple compactifications and black p-branes in Gauss-Bonnet and Lovelock theories, JHEP 05 (2006) 007 [hep-th/0603177] [INSPIRE].
A. Giacomini, J. Oliva and A. Vera, Black strings in Gauss-Bonnet theory are unstable, Phys. Rev. D 91 (2015) 104033 [arXiv:1503.03696] [INSPIRE].
A. Giacomini, C. Henríquez-Báez, M. Lagos, J. Oliva and A. Vera, Instability of black strings in the third-order Lovelock theory, Phys. Rev. D 93 (2016) 104005 [arXiv:1603.02670] [INSPIRE].
T. Kobayashi and T. Tanaka, Five-dimensional black strings in Einstein-Gauss-Bonnet gravity, Phys. Rev. D 71 (2005) 084005 [gr-qc/0412139] [INSPIRE].
P. Suranyi, C. Vaz and L.C.R. Wijewardhana, The fate of black branes in Einstein-Gauss-Bonnet gravity, Phys. Rev. D 79 (2009) 124046 [arXiv:0810.0525] [INSPIRE].
Y. Brihaye, T. Delsate and E. Radu, Einstein-Gauss-Bonnet black strings, JHEP 07 (2010) 022 [arXiv:1004.2164] [INSPIRE].
B. Chen, Z.-Y. Fan, P. Li and W. Ye, Quasinormal modes of Gauss-Bonnet black holes at large D, JHEP 01 (2016) 085 [arXiv:1511.08706] [INSPIRE].
X.-M. Kuang and J.-P. Wu, Thermal transport and quasi-normal modes in Gauss-Bonnet-axions theory, Phys. Lett. B 770 (2017) 117 [arXiv:1702.01490] [INSPIRE].
B. Chen and P.-C. Li, Static Gauss-Bonnet black holes at large D, JHEP 05 (2017) 025 [arXiv:1703.06381] [INSPIRE].
V. Asnin, D. Gorbonos, S. Hadar, B. Kol, M. Levi and U. Miyamoto, High and low dimensions in the black hole negative mode, Class. Quant. Grav. 24 (2007) 5527 [arXiv:0706.1555] [INSPIRE].
R.M. Wald, Black hole entropy is the Noether charge, Phys. Rev. D 48 (1993) R3427 [gr-qc/9307038] [INSPIRE].
T. Harmark and N.A. Obers, General definition of gravitational tension, JHEP 05 (2004) 043 [hep-th/0403103] [INSPIRE].
R. Emparan, T. Harmark, V. Niarchos, N.A. Obers and M.J. Rodriguez, The phase structure of higher-dimensional black rings and black holes, JHEP 10 (2007) 110 [arXiv:0708.2181] [INSPIRE].
B. Chen, P.-C. Li and C.-Y. Zhang, Einstein-Gauss-Bonnet black rings at large D, work in progress.
J. Camps, R. Emparan and N. Haddad, Black brane viscosity and the Gregory-Laflamme instability, JHEP 05 (2010) 042 [arXiv:1003.3636] [INSPIRE].
P. Kovtun, D.T. Son and A.O. Starinets, Holography and hydrodynamics: diffusion on stretched horizons, JHEP 10 (2003) 064 [hep-th/0309213] [INSPIRE].
M. Brigante, H. Liu, R.C. Myers, S. Shenker and S. Yaida, Viscosity bound violation in higher derivative gravity, Phys. Rev. D 77 (2008) 126006 [arXiv:0712.0805] [INSPIRE].
K. Thorne, R. Price and D. MacDonald, Black holes: the membrane paradigm, Yale University Press, New Haven U.S.A., (1986) [INSPIRE].
T. Damour, Black hole eddy currents, Phys. Rev. D 18 (1978) 3598 [INSPIRE].
T. Jacobson, A. Mohd and S. Sarkar, Membrane paradigm for Einstein-Gauss-Bonnet gravity, Phys. Rev. D 95 (2017) 064036 [arXiv:1107.1260] [INSPIRE].
S. Bhattacharyya et al., Currents and radiation from the large D black hole membrane, JHEP 05 (2017) 098 [arXiv:1611.09310] [INSPIRE].
S. Bhattacharyya, P. Biswas, B. Chakrabarty, Y. Dandekar and A. Dinda, The large D black hole dynamics in AdS/dS backgrounds, arXiv:1704.06076 [INSPIRE].
M. Rozali, E. Sabag and A. Yarom, Holographic turbulence in a large number of dimensions, arXiv:1707.08973 [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1707.09766
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Chen, B., Li, PC. & Zhang, CY. Einstein-Gauss-Bonnet black strings at large D . J. High Energ. Phys. 2017, 123 (2017). https://doi.org/10.1007/JHEP10(2017)123
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP10(2017)123